$\begin{equation*} \begin{cases} 4x - 3y = 12 &\\ 3x + 4y = 34 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 4x - 3y = 12 &\\ 4y = 34 - 3x & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 4x - 3y = 12 &\\ y = 8,5 - 0,75x & \end{cases} \end{equation*}$
4x − 3y = 12
4x − 3 * (8,5 − 0,75x) = 12
4x − 25,5 + 2,25x = 12
6,25x = 12 + 25,5
6,25x = 37,5
x = 37,5 : 6,25
x = 6
y = 8,5 − 0,75x = 8,5 − 0,75 * 6 = 8,5 − 4,5 = 4
Ответ: (6;4)

$\begin{equation*} \begin{cases} -5x + 2y = 20 &\\ 2x - 5y = -8 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 2y = 5x + 20 &\\ 2x - 5y = -8 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} y = 2,5x + 10 &\\ 2x - 5y = -8 & \end{cases} \end{equation*}$
2x − 5 * (2,5x + 10) = −8
2x − 12,5x − 50 = −8
−10,5x = −8 + 50
−10,5x = 42
x = 42 : (−10,5)
x = −4
y = 2,5x + 10 = 2,5 * (−4) + 10 = −10 + 10 = 0
Ответ: (−4;0)

$\begin{equation*} \begin{cases} 2x - 3y = 12 &\\ 3x + 2y = 5 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 2x - 3y = 12 &\\ 2y = 5 - 3x & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 2x - 3y = 12 &\\ y = 2,5 - 1,5x & \end{cases} \end{equation*}$
2x − 3 * (2,5 − 1,5x) = 12
2x − 7,5 + 4,5x = 12
6,5x = 12 + 7,5
6,5x = 19,5
x = 19,5 : 6,5
x = 3
y = 2,5 − 1,5x = 2,5 − 1,5 * 3 = 2,5 − 4,5 = −2
Ответ: (3;−2)

$\begin{equation*} \begin{cases} 5x - 4y = 5 &\\ 2x - 3y = 9 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 5x - 4y = 5 &\\ 2x = 3y + 9 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 5x - 4y = 5 &\\ x = 1,5y + 4,5 & \end{cases} \end{equation*}$
5x − 4y = 5
5 * (1,5y + 4,5) − 4y = 5
7,5y + 22,5 − 4y = 5
3,5y = 5 − 22,5
3,5y = −17,5
y = −17,5 : 3,5
y = −5
x = 1,5y + 4,5 = 1,5 * (−5) + 4,5 = −7,5 + 4,5 = −3
Ответ: (−3;−5)